Sure, let's combine the like terms step-by-step to find the equivalent expression for the given terms:
[tex]\[
\frac{9}{8} m + \frac{9}{10} - 2 m - \frac{3}{5}
\][/tex]
1. Combine the [tex]\(m\)[/tex] terms:
We have [tex]\(\frac{9}{8} m\)[/tex] and [tex]\(-2 m\)[/tex]. Combining these terms:
[tex]\[
\frac{9}{8} m - 2 m
\][/tex]
Converting [tex]\(2 m\)[/tex] to a fraction with the same denominator as [tex]\(\frac{9}{8}\)[/tex] (which is 8):
[tex]\[
2 m = \frac{16}{8} m
\][/tex]
Now, subtract the two fractions:
[tex]\[
\frac{9}{8} m - \frac{16}{8} m = \frac{9 - 16}{8} m = -\frac{7}{8} m
\][/tex]
2. Combine the constant terms:
We have [tex]\(\frac{9}{10}\)[/tex] and [tex]\(-\frac{3}{5}\)[/tex]. First, convert [tex]\(-\frac{3}{5}\)[/tex] to a fraction with denominator 10 (since [tex]\(\frac{9}{10}\)[/tex] already has a denominator of 10):
[tex]\[
-\frac{3}{5} = -\frac{3 \times 2}{5 \times 2} = -\frac{6}{10}
\][/tex]
Now, combine the two fractions:
[tex]\[
\frac{9}{10} - \frac{6}{10} = \frac{9 - 6}{10} = \frac{3}{10}
\][/tex]
3. Form the final expression by combining both the results from steps 1 and 2:
[tex]\[
-\frac{7}{8}m + \frac{3}{10}
\][/tex]
Thus, the equivalent expression is:
[tex]\[
-\frac{7}{8} m + \frac{3}{10}
\][/tex]
